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8 tháng 8 2017

Ta có:

\(\frac{3}{2.7}+\frac{3}{7.12}+\frac{3}{12.17}+...+\frac{3}{82.87}\)

\(=\frac{3}{5}.\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{82}-\frac{1}{87}\right)\)

\(=\frac{3}{5}.\left(\frac{1}{2}-\frac{1}{87}\right)=\frac{3}{5}.\frac{85}{174}=\frac{17}{58}\)

Ta có: 

A = \(\frac{3}{2.7}+\frac{3}{7.12}+\frac{3}{12.17}+...+\frac{3}{82.87}\)( dấu chấm là dấu nhân nhá, lên lớp 6 thì bạn sẽ biết )

\(\frac{5}{3}.A=\frac{5}{3}.\left(\frac{3}{2.7}+\frac{3}{7.12}+\frac{3}{12.17}+...+\frac{3}{82.87}\right)\)

\(\frac{5}{3}.A=\frac{5}{2.7}+\frac{5}{7.12}+\frac{5}{12.17}+...+\frac{5}{82.87}\)

\(\frac{5}{3}.A=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}+\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{82}-\frac{1}{87}\)

\(\frac{5}{3}.A=\frac{1}{2}-\frac{1}{87}\)

\(\frac{5}{3}.A=\frac{85}{174}\)

\(A=\frac{85}{174}:\frac{5}{3}=\frac{17}{58}\)

                                             Đ/s : \(\frac{17}{58}\)

Ủng hộ mik nhá !!!

10 tháng 8 2017

các bn ơi cố giúp mik nha 

10 tháng 8 2017

làm cách thủ công đi

\(=\frac{20}{69}\)

10 tháng 8 2017

\(\frac{4}{3.7}+\frac{5}{7.12}+\frac{1}{12.13}+\frac{7}{13.20}+\frac{3}{20.23}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{20}-\frac{1}{23}=\frac{1}{3}-\frac{1}{23}=\frac{20}{69}\)

14 tháng 7 2017

\(\frac{4}{3\cdot7}+\frac{5}{7.12}+..+\frac{8}{20\cdot28}\)

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{20}-\frac{1}{28}\)

\(=\frac{1}{3}-\frac{1}{28}+0+...+0\)

\(=\frac{25}{84}\)

14 tháng 7 2017

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{20}-\frac{1}{28}\)

\(=\frac{1}{3}-\frac{1}{28}\)

\(=\frac{25}{84}\)

29 tháng 7 2018

\(\frac{2}{5\cdot7}+\frac{5}{7\cdot12}+\frac{8}{12\cdot20}+\frac{3}{140}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{20}+\frac{3}{140}\)

\(=\frac{1}{5}-\frac{1}{20}+\frac{3}{140}\)

\(=\frac{3}{20}+\frac{3}{140}=\frac{6}{35}\)

29 tháng 7 2018

\(\frac{2}{5.7}\)\(\frac{5}{7.12}\)\(\frac{8}{12.20}\)\(\frac{3}{140}\).

\(\frac{1}{5}\)\(\frac{1}{7}\)\(\frac{1}{7}\)\(\frac{1}{12}\)\(\frac{1}{12}\)\(\frac{1}{20}\)\(\frac{3}{140}\).

\(\frac{1}{5}\)\(\frac{1}{20}\)\(\frac{3}{140}\).

\(\frac{20}{100}\)\(\frac{5}{100}\)\(\frac{3}{140}\).

\(\frac{15}{100}\)\(\frac{3}{140}\).

\(\frac{3}{20}\)\(\frac{3}{140}\).

\(\frac{21}{140}\)\(\frac{3}{140}\).

\(\frac{24}{140}\).

\(\frac{6}{35}\).

7 tháng 5 2018

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

\(=1-\frac{1}{11}\)

\(=\frac{11}{11}-\frac{1}{11}\)

\(=\frac{10}{11}\)

Chúc bạn học tốt !!! 

7 tháng 5 2018

10/11 là   đúng 

26 tháng 3 2018

\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\right)\)

=\(2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)

=\(2\left(1-\frac{1}{21}\right)\)

=\(\frac{2.20}{21}=\frac{40}{21}\)

1 tháng 3 2019

a) \(C=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{73.76}\)

\(C=1.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{73}-\frac{1}{76}\right)\)

\(C=1.\left(\frac{1}{4}-\frac{1}{76}\right)\)

\(C=1.\frac{9}{38}\)

\(C=\frac{9}{38}\)

b) \(D=\frac{5}{10.11}+\frac{5}{11.12}+\frac{5}{12.13}+...+\frac{5}{99.100}\)

\(D=5.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{99}+\frac{1}{100}\right)\)

\(D=5.\left(\frac{1}{10}-\frac{1}{100}\right)\)

\(D=5.\frac{9}{100}\)

\(D=\frac{99}{20}\)

3 tháng 5 2018

a) \(A=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+...+\frac{1}{25\cdot27\cdot29}\)

   \(\Rightarrow4A=\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+...+\frac{4}{25\cdot27\cdot29}\)

\(\Rightarrow4A=\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5\cdot7}+...+\frac{1}{25\cdot27}-\frac{1}{27\cdot29}\)

\(\Rightarrow4A=\frac{1}{1\cdot3}-\frac{1}{27\cdot29}=\frac{1}{3}-\frac{1}{783}=\frac{261}{783}-\frac{1}{783}=\frac{260}{783}\)

\(\Rightarrow A=\frac{\frac{260}{783}}{4}=\frac{65}{783}\)

b) \(\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\)

\(\Rightarrow100\cdot\left(\frac{1}{1\cdot101}+\frac{1}{2\cdot102}+...+\frac{1}{10\cdot110}\right)x=100\cdot\left(\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+...+\frac{1}{100\cdot110}\right)\)

\(\Rightarrow\left(\frac{100}{1\cdot101}+\frac{100}{2\cdot102}+...+\frac{100}{10\cdot110}\right)x=10\cdot\left(\frac{10}{1\cdot11}+\frac{10}{2\cdot12}+...+\frac{10}{100\cdot110}\right)\)

\(\Rightarrow\left(1-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\right)x=10\cdot\left(1-\frac{1}{10}+\frac{1}{2}-\frac{1}{12}+...+\frac{1}{100}-\frac{1}{110}\right)\)

\(\Rightarrow\left(1-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\right)x=10\cdot\left(1-\frac{1}{101}+\frac{1}{2}-\frac{1}{102}+...+\frac{1}{10}-\frac{1}{110}\right)\)

\(\Rightarrow x=10\cdot\)

28 tháng 6 2017

CÂU 1 = -59/111

 CÂU 2 = 11/63

     

28 tháng 6 2017

cảm ơn kết quả thì mik b òi nhưng mik cần cách làm